In an isosceles right-angled triangle ABC (angle B-line) Drawn height BD Find the angles of the triangle

Since triangle ABC is isosceles, the angles at its base are equal. Find the angles at the base, assuming that the sum of the angles of the triangle is 180 °:

∠BAC = ∠BCA = (180 ° – 90 °) / 2 = 45 °.

The height BD, since the triangle is isosceles, divides it into two equal triangles – ABD and BDC, it is also the bisector of the right angle B (or angle ABC).

Thus, ∠ABD = ∠DBC = 90 ° / 2;

∠ABD = ∠DBC = 45 °.

BD is the height of the triangle, it is perpendicular to the AC side, so ∠ADB = ∠BDC = 90 °.